PXI-6570 to floating DUT Vss

Hello,

I have a DUT with a ground that is floating 3.3V above earth ground.  Vss of the DUT is set to -3.3V (relative to DUT gnd) which makes Vss equivalent to earth ground.  Can I hook the 6570 ground pins to DUT Vss without harming the 6570 functionality?  The idea is to allow me to use the 6570 with positive logic voltage levels, relative to earth ground, but the DUT would see negative voltage levels relative to DUT ground.  My requirements are V_IL< -3V and V_IH> -1V.